Theorem erALTVeq1i

Description: Equality theorem for equivalence relation on domain quotient, inference version. (Contributed by Peter Mazsa, 25-Sep-2021)

	Ref	Expression
Hypothesis	erALTVeq1i.1	⊢ 𝑅 = 𝑆
Assertion	erALTVeq1i	⊢ ( 𝑅 ErALTV 𝐴 ↔ 𝑆 ErALTV 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		erALTVeq1i.1	⊢ 𝑅 = 𝑆
2		erALTVeq1	⊢ ( 𝑅 = 𝑆 → ( 𝑅 ErALTV 𝐴 ↔ 𝑆 ErALTV 𝐴 ) )
3	1 2	ax-mp	⊢ ( 𝑅 ErALTV 𝐴 ↔ 𝑆 ErALTV 𝐴 )